Memory and CPU efficient computation of the Fresnel free-space propagator in Fourier optics simulations

We describe a version of the paraxial free-space Fourier optics propagator for numerical wave propagation simulations that eliminates the need for a dense sampling of an input electric field with phase dominated by quadratic terms developing at some distance from the source or from the radiation beam waist. This propagator requires considerably (two to three orders of magnitude as observed in routine simulations) less memory and CPU resources than the standard Fresnel free-space propagator while preserving its levels of accuracy and generality. This method has been successfully used in "Synchrotron Radiation Workshop" code for more than a decade. It has greatly contributed to the applicability of the code, and more generally the applicability of the Fourier optics methods, to wave-optics based simulations of radiation propagation through optical systems of beamlines at high-brightness and high-coherence synchrotron light sources.